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Gravitational instantons with faster than quadratic curvature decay (II)

Gao Chen ORCID logo and Xiuxiong Chen

Abstract

This is our second paper in a series to study gravitational instantons, i.e. complete hyperkähler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: (i) The asymptotic rate of gravitational instantons to the standard models can be improved automatically. (ii) Any ALF-Dk gravitational instanton must be the Cherkis–Hitchin–Ivanov–Kapustin–Lindström–Roček metric.

Funding source: National Science Foundation

Award Identifier / Grant number: 1515795

Funding statement: The second author is partially supported by the National Science Foundation through grant no. 1515795.

Acknowledgements

Both authors are grateful to the insightful and helpful discussions with Sir Simon Donaldson, Blaine Lawson, Claude LeBrun and Martin Roček. We also thank the referees and editors for polishing our article.

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Received: 2016-12-09
Published Online: 2017-06-03
Published in Print: 2019-11-01

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